Award #: N00014-05-1-0414

1. Application of multidimensional Fourier analysis for the extremely fast numerical integration of the partial differential equations of surface water waves is the long-term goal of this work. The approach is a generalization of linear Fourier analysis and therefore is a hyperfast extension of the fast Fourier transform (FFT) to the nonlinear Euler water wave equations. 2. The present report discusses progress made in both the shallow and deep-water environments, anticipating the marriage of the two in the coming year for a complete, higher order, hyperfast integration to Euler. An important application of the approach is possibility of the on-board computation of wave properties as derived from shipboard direct wave and/or radar measurements of the sea surface, leading to prediction of sea state conditions, including the presence of rogue waves in real time. OBJECTIVES 1. The objective of the present research program is the development of fast numerical multidimensional Fourier techniques applied to a wide range of wave modeling and analysis problems. 2. Important progress made in the past year has been the development of three new algorithms for multidimensional Fourier analysis. These algorithms are the key to future hyperfast applications of the method